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Type:

Package

Title:

S-LASSO Estimator for the Function-on-Function Linear Regression

Version:

1.0.0

Description:

Implements the smooth LASSO estimator for the function-on-function linear regression model described in Centofanti et al. (2020) <doi:10.48550/arXiv.2007.00529>.

License:

GPL (≥ 3)

Encoding:

UTF-8

RoxygenNote:

7.1.2

LinkingTo:

Rcpp, RcppArmadillo

Depends:

inline

Imports:

Rcpp, RcppArmadillo, fda, fda.usc, matrixcalc, parallel, matrixStats, MASS, plot3D, methods, cxxfunplus

URL:

https://github.com/unina-sfere/slasso

BugReports:

https://github.com/unina-sfere/slasso

SystemRequirements:

GNU make

Suggests:

knitr, rmarkdown, testthat

NeedsCompilation:

yes

Packaged:

2021-10-14 12:23:55 UTC; fabio

Author:

Fabio Centofanti [cre, aut], Antonio Lepore [aut], Simone Vantini [aut], Matteo Fontana [aut]

Maintainer:

Fabio Centofanti <fabio.centofanti@unina.it>

Repository:

CRAN

Date/Publication:

2021-10-15 07:40:02 UTC

Smooth LASSO Estimator for the Function-on-Function Linear Regression Model

Description

Implements the Smooth LASSO Estimator for the Function-on-Function Linear Regression Model described in Centofanti et al. (2020) <arXiv:2007.00529>.

Details

Package:	slasso
Type:	Package
Version:	1.0.0
Date:	2021-10-13
License:	GPL (>= 3)

Author(s)

Fabio Centofanti, Matteo Fontana, Antonio Lepore, Simone Vantini

References

Centofanti, F., Fontana, M., Lepore, A., & Vantini, S. (2020). Smooth LASSO Estimator for the Function-on-Function Linear Regression Model. arXiv preprint arXiv:2007.00529.

Examples


library(slasso)
data<-simulate_data("Scenario II",n_obs=150)
X_fd=data$X_fd
Y_fd=data$Y_fd
domain=c(0,1)
n_basis_s<-30
n_basis_t<-30
breaks_s<-seq(0,1,length.out = (n_basis_s-2))
breaks_t<-seq(0,1,length.out = (n_basis_t-2))
basis_s <- fda::create.bspline.basis(domain,breaks=breaks_s)
basis_t <- fda::create.bspline.basis(domain,breaks=breaks_t)

mod_slasso_cv<-slasso.fr_cv(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L_vec = 10^seq(0,1,by=1),lambda_s_vec = 10^-9,lambda_t_vec = 10^-7,
B0=NULL,max_iterations=10,K=2,invisible=1,ncores=1)
mod_slasso<-slasso.fr(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L = 10^0.7,lambda_s =10^-5,lambda_t = 10^-6,B0 =NULL,invisible=1,max_iterations=10)

plot(mod_slasso_cv)
plot(mod_slasso)

Plot the results of the S-LASSO method

Description

This function provides plots of the S-LASSO coefficient function estimate when applied to the output of slasso.fr, whereas provides the cross-validation plots when applied to the output of slasso.fr_cv. In the latter case the first plot displays the CV values as a function of lambda_L, lambda_s and lambda_t, and the second plot displays the CV values as a function of lambda_L with lambda_s and lambda_t fixed at their optimal values.

Usage

## S3 method for class 'slasso_cv'
plot(x, ...)

## S3 method for class 'slasso'
plot(x, ...)

Arguments

x

The output of either slasso.fr_cv or slasso.fr.

...

No additional parameters, called for side effects.

Value

No return value, called for side effects.

Examples

library(slasso)
data<-simulate_data("Scenario II",n_obs=150)
X_fd=data$X_fd
Y_fd=data$Y_fd
domain=c(0,1)
n_basis_s<-30
n_basis_t<-30
breaks_s<-seq(0,1,length.out = (n_basis_s-2))
breaks_t<-seq(0,1,length.out = (n_basis_t-2))
basis_s <- fda::create.bspline.basis(domain,breaks=breaks_s)
basis_t <- fda::create.bspline.basis(domain,breaks=breaks_t)
mod_slasso<-slasso.fr(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L = -1.5,lambda_s =-8,lambda_t = -7,B0 =NULL,invisible=1,max_iterations=10)
plot(mod_slasso)

Simulate data through the function-on-function linear regression model

Description

Generate synthetic data as in the simulation study of Centofanti et al. (2020).

Usage

simulate_data(scenario, n_obs = 3000, type_x = "Bspline")

Arguments

scenario

A character strings indicating the scenario considered. It could be "Scenario I", "Scenario II", "Scenario III", and "Scenario IV".

n_obs

Number of observations.

type_x

Covariate generating mechanism, either Bspline or Brownian.

Value

A list containing the following arguments:

X: Covariate matrix, where the rows correspond to argument values and columns to replications.

Y: Response matrix, where the rows correspond to argument values and columns to replications.

X_fd: Coavariate functions.

Y_fd: Response functions.

clus: True cluster membership vector.

References

Centofanti, F., Fontana, M., Lepore, A., & Vantini, S. (2020). Smooth LASSO Estimator for the Function-on-Function Linear Regression Model. arXiv preprint arXiv:2007.00529.

Examples

library(slasso)
data<-simulate_data("Scenario II",n_obs=150)

Smooth LASSO estimator for the function-on-function linear regression model

Description

The smooth LASSO (S-LASSO) method for the function-on-function linear regression model provides interpretable coefficient function estimates that are both locally sparse and smooth (Centofanti et al., 2020).

Usage

slasso.fr(
  Y_fd,
  X_fd,
  basis_s,
  basis_t,
  lambda_L,
  lambda_s,
  lambda_t,
  B0 = NULL,
  ...
)

Arguments

Y_fd

An object of class fd corresponding to the response functions.

X_fd

An object of class fd corresponding to the covariate functions.

basis_s

B-splines basis along the s-direction of class basisfd.

basis_t

B-splines basis along the t-direction of class basisfd.

lambda_L

Regularization parameter of the functional LASSO penalty.

lambda_s

Regularization parameter of the smoothness penalty along the s-direction.

lambda_t

Regularization parameter of the smoothness penalty along the t-direction.

B0

Initial estimator of the basis coefficients matrix of the coefficient function. Should have dimensions in accordance with the basis dimensions of basis_s and basis_t.

...

Other arguments to be passed to the Orthant-Wise Limited-memory Quasi-Newton optimization function. See the lbfgs help page of the package lbfgs.

Value

A list containing the following arguments:

B: The basis coefficients matrix estimate of the coefficient function.
Beta_hat_fd: The coefficient function estimate of class bifd.
alpha: The intercept function estimate.
lambdas_L: Regularization parameter of the functional LASSO penalty.
lambda_s: Regularization parameter of the smoothness penalty along the s-direction.
lambda_t: Regularization parameter of the smoothness penalty along the t-direction.
Y_fd: The response functions.
X_fd: The covariate functions.
per_0: The fraction of domain where the coefficient function is zero.
type: The output type.

References

Centofanti, F., Fontana, M., Lepore, A., & Vantini, S. (2020). Smooth LASSO Estimator for the Function-on-Function Linear Regression Model. arXiv preprint arXiv:2007.00529.

Examples

library(slasso)
data<-simulate_data("Scenario II",n_obs=150)
X_fd=data$X_fd
Y_fd=data$Y_fd
domain=c(0,1)
n_basis_s<-30
n_basis_t<-30
breaks_s<-seq(0,1,length.out = (n_basis_s-2))
breaks_t<-seq(0,1,length.out = (n_basis_t-2))
basis_s <- fda::create.bspline.basis(domain,breaks=breaks_s)
basis_t <- fda::create.bspline.basis(domain,breaks=breaks_t)
mod_slasso<-slasso.fr(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L = -1.5,lambda_s =-8,lambda_t = -7,B0 =NULL,invisible=1,max_iterations=10)

Cross-validation for the S-LASSO estimator

Description

K-fold cross-validation procedure to choose the tuning parameters for the S-LASSO estimator (Centofanti et al., 2020).

Usage

slasso.fr_cv(
  Y_fd,
  X_fd,
  basis_s,
  basis_t,
  K = 10,
  kss_rule_par = 0.5,
  lambda_L_vec = NULL,
  lambda_s_vec = NULL,
  lambda_t_vec = NULL,
  B0 = NULL,
  ncores = 1,
  ...
)

Arguments

Y_fd

An object of class fd corresponding to the response functions.

X_fd

An object of class fd corresponding to the covariate functions.

basis_s

B-splines basis along the s-direction of class basisfd.

basis_t

B-splines basis along the t-direction of class basisfd.

K

Number of folds. Default is 10.

kss_rule_par

Parameter of the k-standard error rule. If kss_rule_par=0 the tuning parameters that minimize the estimated prediction error are chosen. Default is 0.5.

lambda_L_vec

Vector of regularization parameters of the functional LASSO penalty.

lambda_s_vec

Vector of regularization parameters of the smoothness penalty along the s-direction.

lambda_t_vec

Vector of regularization parameters of the smoothness penalty along the t-direction.

B0

Initial estimator of the basis coefficients matrix of the coefficient function. Should have dimensions in accordance with the basis dimensions of basis_s and basis_t.

ncores

If ncores>1, then parallel computing is used, with ncores cores. Default is 1.

...

Other arguments to be passed to the Orthant-Wise Limited-memory Quasi-Newton optimization function. See the lbfgs help page of the package lbfgs.

Value

A list containing the following arguments:

lambda_opt_vec: Vector of optimal tuning parameters.
CV: Estimated prediction errors.
CV_sd: Standard errors of the estimated prediction errors.
per_0: The fractions of domain where the coefficient function is zero for all the tuning parameters combinations.
comb_list: The combinations of lambda_L,lambda_s and lambda_t explored.
Y_fd: The response functions.
X_fd: The covariate functions.

References

Centofanti, F., Fontana, M., Lepore, A., & Vantini, S. (2020). Smooth LASSO Estimator for the Function-on-Function Linear Regression Model. arXiv preprint arXiv:2007.00529.

Examples

library(slasso)
data<-simulate_data("Scenario II",n_obs=150)
X_fd=data$X_fd
Y_fd=data$Y_fd
domain=c(0,1)
n_basis_s<-60
n_basis_t<-60
breaks_s<-seq(0,1,length.out = (n_basis_s-2))
breaks_t<-seq(0,1,length.out = (n_basis_t-2))
basis_s <- fda::create.bspline.basis(domain,breaks=breaks_s)
basis_t <- fda::create.bspline.basis(domain,breaks=breaks_t)
mod_slasso_cv<-slasso.fr_cv(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L_vec=seq(0,1,by=1),lambda_s_vec=c(-9),lambda_t_vec=-7,B0=NULL,
max_iterations=10,K=2,invisible=1,ncores=1)

Smooth LASSO Estimator for the Function-on-Function Linear Regression Model

Description

Details

Author(s)

References

See Also

Examples

Plot the results of the S-LASSO method

Description

Usage

Arguments

Value

Examples

Simulate data through the function-on-function linear regression model

Description

Usage

Arguments

Value

References

Examples

Smooth LASSO estimator for the function-on-function linear regression model

Description

Usage

Arguments

Value

References

See Also

Examples

Cross-validation for the S-LASSO estimator

Description

Usage

Arguments

Value

References

See Also

Examples